Q:

# PLEASE HELP ASAP!A line is drawn so that it passes through the points (-3,-1) and (4,2). a. What is the slope of the line?b. Using the point (4,2) and the slope found above, write the equation of the line in point-slope form.Please write out how you got your answer or the steps you took.

Accepted Solution

A:
A) To find slope, use the equation:$$slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}}$$where $$x_{2}$$ and $$y_{2}$$ are the x and y values of one coordinate point , and $$x_{1}$$ and $$y_{1}$$ are the x and y values of another coordinate point . Since we are given two coordinate points, (-3,-1) and (4,2), that means we can find the slope using the slope equation.
Let's choose (4, 2) as your $$(x_{2}, y_{2})$$ point and (-3, -1) as your $$(x_{1}, y_{1})$$ point, but you can switch those if you want! That makes $$x_{2} = 4, y_{2} = 2$$ and $$x_{1} = -3, y_{1} = -1$$. Plug these values into the slope equation:
$$slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}} \\ slope = \frac{2-(-1)}{4-(-3)} \\ slope = \frac{3}{7}$$

The slope of the line is 3/7.

B) Remember that the general equation for point-slope form is $$y - y_1 = m(x - x_1)$$, where m = the slope, $$x_{1}$$ = the x value of a coordinate point $$(x_{1}, y_{2})$$ on the line, and $$y_{1}$$ = the y value of the same coordinate point on the line.

You are given (4, 2) as one of the coordinate points. That means $$x_{1}$$ = 4 and $$y_{1}$$ = 2. We found the slope, m = $$\frac{3}{7}$$ in part A. Now plug these values into the general equation for point-slope form to find your point-slope form equation:
$$y - y_1 = m(x - x_1)\\ y - 2 = \frac{3}{7}(x - 4)$$

Your point-slope form equation is $$y - 2 = \frac{3}{7}(x - 4)$$.